Munich Personal RePEc Archive Strategic Trade and Privatization Policies in Bilateral Mixed Markets Xu, Lili and Lee, Sang-Ho and Wang, Leonard Dalian Maritime University, Chonnam National University, Zhongnan University of Economics and Law 24 July 2017 Online at https://mpra.ub.uni-muenchen.de/80340/ MPRA Paper No. 80340, posted 26 Jul 2017 14:57 UTC
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Munich Personal RePEc Archive
Strategic Trade and Privatization
Policies in Bilateral Mixed Markets
Xu, Lili and Lee, Sang-Ho and Wang, Leonard
Dalian Maritime University, Chonnam National University,
Zhongnan University of Economics and Law
24 July 2017
Online at https://mpra.ub.uni-muenchen.de/80340/
MPRA Paper No. 80340, posted 26 Jul 2017 14:57 UTC
Strategic Trade and Privatization Policies in Bilateral Mixed Markets
Lili Xu
Department of Economics and Trade, Dalian Maritime University, China
Sang-Ho Lee*
School of Economics, Chonnam National University, Korea
Leonard F.S. Wang
Wenlan School of Business, Zhongnan University of Economics and Law, China
We consider strategic trade and privatization policies in international bilateral mixed markets where a
domestic state-owned enterprise competes with both domestic and foreign private enterprises in each
country. We examine the strategic interaction of two countries’ optimal choices of privatization and
trade policies with different combinations of production subsidy and import tariff, and find some
interesting policy implications. First, a higher social welfare can be achieved with the appropriate
degree of privatization when both governments adopt a production subsidy only. Second, FTA can
work as a coordination device to solve the prisoner’s dilemma problem. Third, the maximum-revenue
privatization, combined with zero subsidy and higher tariff, is higher than optimum-welfare
privatization. Finally, the international bilateral equilibrium needs less degree of privatization and
lower subsidy rate, even though it is jointly suboptimal from the viewpoint of global welfare.
Keywords: strategic privatization; international bilateral mixed market; industrial policy; optimal
tariff;
JEL classifications: L32; D43; F12
1. Introduction
Since the 1980s, many developed and developing countries have continued to privatize their
state-owned enterprises (SOEs) under the global trends of trade liberalization.1 Yet, SOEs are
strongly concentrated in a few strategic sectors and thus, they still control large portions of the world’s
resources.2 Over half (in values terms) of all SOEs in OECD countries are significant players in
sectors such as transportation, telecommunications, power generation, electricity, finance,
manufacturing, and other energy industries. Along with the open economy and trade liberalization,
such as negotiations for joining the WTO or establishing free trade areas, FTA has also inspired
foreign firms’ entry into those industries, even with the existence of SOEs.3
*Correspondence: Sang-Ho Lee, Professor, Department of Economics, Chonnam National University, Yongbong-Road 77,
Bukgu, Gwangju 500-757 Korea. Tel: 82-62-530-1553, Fax: 82-62-530-1559, E-mail: [email protected]. 1 Nellis (1999) showed that from 1980 to 1991, roughly 6,800 medium and large scale SOEs were privatized in non-
transition economies while 60,000 such companies were privatized in transition economies, including hundreds of thousands
of small SOEs. See also Lee et al. (2013) for more discussions on world-wide trend on privatization. 2 According to OECD report by Kowalski et al. (2013), among the 2000 largest public companies in the world, over 10%
SOEs have significant government ownership and their sales are equivalent to approximately 6% of worldwide GDP. See
also Xu et al. (2016) for more discussions on the important role of SOE. 3 According to the WTO (2015), the regional trade agreements (RTAs) which are reciprocal agreements on trade between
two or more partners are the prominent feature of international trade. For example, among 406 RTAs which are in force
from 1970 to 2015 in the world, the number of FTAs is 232, i.e., more than half of the countries choose to join the FTA. The
annual increase of new FTAs is over ten percent from 1990s in the worldwide. As of 2014, 227 FTAs are in force and more
1
Although existing literature suggests that there are some gains in the efficiency of a privatized
firm, researchers in the fields of industrial organization, international trade and development
economics, and especially those who are interested in the privatization of the SOE, want to further
explore how the foreign competition affects the desirability of privatization in mixed markets where
the SOE competes with domestic and foreign private firms. In particular, economic studies on how to
substantially reset production subsidy and import tariff are still increasingly important.
The economic modelling of a mixed oligopoly with domestic and foreign competitors begins
with Fjell and Pal (1996), who investigated the effect of introducing foreign private firms on the
equilibrium price and allocation of production. White (1996) introduced the production subsidy into
the mixed market and found that welfare is unchanged by privatization if subsidies are used before
and after privatization. This privatization neutrality theorem was supported by Tomaru (2006) and
Kato and Tomaru (2007), who showed that the optimal subsidy, all firms’ output, profits and social
welfare are identical regardless of the share in a SOE and the objectives of the firms. However,
Matsumura and Tomaru (2012) showed that privatization matters on the welfare even under the
optimal tax-subsidy policy if there are foreign competitors.
Other theoretical literature has analyzed import tariff in an international mixed market. Chang
(2005) examined a mixed duopoly model with a more efficient foreign firm under Cournot and
Stackelberg competition, and showed that the optimal level of privatization depends crucially upon
the strategic substitutability-complementarity assumption. Chao and Yu (2006) found that foreign
competition lowers the optimal tariff rate but partial privatization raises it. Wang et al. (2012)
examined the effect of privatization on the priority of the maximum revenue tariff and the optimum-
welfare tariff under Cournot and Stackelberg competitions, and showed that the optimum-welfare
tariff will be lower than the maximum-revenue tariff regardless of the order of firms’ move when the
asymmetric marginal cost of the privatized firm is higher than a critical value.
Some studies simultaneously consider the relations between privatization policy and dual trade
instruments, production subsidy or/and import tariff, in a mixed market. Pal and White (1998)
examined the interaction between privatization and strategic trade policies, and found that the welfare
is always increased with privatization if production subsidy is used only. However, privatization
increases welfare over much of the parameter space if import tariff is used only. Pal and White (2003)
also showed that the existence of SOE lowers optimal tariffs and subsidies, but also lowers the total
volume of trade between the two countries. The lower volume of trade, however, does not translate
into lower levels of welfare for the trading countries. Chang (2007), Yu and Lee (2011), and Han
(2012) examined the optimal privatization and trade policies in an international mixed market and
showed that full nationalization is the best choice under Cournot competition, but the privatization
strategy is affected strongly by trade instruments and cost difference between firms. Wang et al. (2014)
examined privatization policy and entry regulation in a mixed oligopoly market with foreign
competitors and free entry. It demonstrated that as long as the entry cost is relatively lower, domestic
entry is socially excessive whether it is free trade or the domestic government imposes the tariff policy.
Wang and Chiou (2015) showed that the welfare effect of privatization will be affected by the trade
liberalization policy, and the optimum-welfare tariff and privatization should be higher in the presence
of subsidy policy of foreign country than those in the absence of subsidy policy.
FTAs are in the process of being enacted. The well-known inter-regional economic cooperation agreements on FTAs include
the European Economic Community (EEC), North American Free Trade Agreement (NAFTA), Southern Common Market
(MERCOSUR), and ASEAN Free Trade Area.
2
All those previous studies have still explored the relationship between privatization and trade
policy in a unilateral mixed market framework, where the domestic SOE competes with domestic and
foreign firms in the home country. However, as FTA has recently inspired foreign competition into
domestic market, the strategic interaction between two governments becomes increasing and more
important. The emergence of FTA requires the study on the further analysis of strategic trade policies
in the context of international bilateral trade model.
In the strategic trade literature, Brander and Spencer (1984, 1985) firstly showed that
government could improve its terms of trade through tariff or subsidy to take a leader position
transferring a foreign firm’s revenue to a domestic firm. Eaton and Grossman (1986) and Collie
(1993) also analyzed the welfare effects of trade and industrial policies for a range of specifications of
an oligopolistic industry and cost asymmetry. Van Long and Stähler (2009) examined that the home
government can simultaneously subsidize domestic firms and impose tariffs. It is well-known
proposition of trade theory that in the absence of directly trade-related distortions or policy goals,
subsidies are superior to tariffs for achieving any economic objective in the pure oligopolistic market.
On the other hand, Barcena-Ruiz and Garzon (2005) firstly considered an international integrated
mixed market, comprising of two countries. Assuming that SOEs are less efficient than private firms,
they obtained that when the marginal cost of the SOE takes an intermediate value, each government
wants the government of the other country to privatize its SOE. In this case, only one government
privatizes and that government obtains lower social welfare. Dadpay and Heywood (2006) showed
that two competing (domestic and foreign) SOEs play the role of trade barriers and the strategic
interaction of the two governments usually serves to reduce welfare. Han and Ogawa (2008), Lee et al.
(2013) and Xu and Lee (2015) incorporated import tariff and examined the interaction of two
countries regarding strategic choices of privatization policy and import tariff. They demonstrated that
the equilibrium degree of privatization depends not only on the relative efficiency of the SOE, but
also on choice of trade policy.
In this paper, we consider an international bilateral mixed market where a domestic state-owned
enterprise competes with both domestic and foreign private enterprises in the context of intra-industry
trade. We examine the strategic interaction of two countries’ optimal choices on trade instruments and
privatization policy. Specifically, we investigate two different options of production subsidy and
import tariff, coupled with partial privatization, and demonstrate the following main results.
First, under Cournot competition, a higher social welfare can be achieved when both
governments adopt a production subsidy instrument with partial privatization in international bilateral
mixed markets. This is contrasted to the previous results under a unilateral mixed market, such as Yu
and Lee (2011) and Han (2012), in which the dual trade instruments of subsidy and tariff with full
nationalization is the best choice. Second, when the SOE take a leader position under Stackelberg
competition, except for the optimal degrees of privatization, the optimal levels of subsidy, tariff and
social welfare are the same with those under Cournot competition. This is interesting in that as far as
the optimal degree of privatization is well chosen, the social welfare is independent of the leadership
power of the SOE in each country. Third, irrespective of whether symmetric or asymmetric choices of
two countries on trade instruments between subsidy and tariff, we show that FTA can work as a
coordination device to solve the prisoner’s dilemma, where both countries could achieve higher social
welfare if they cooperate and adopt a subsidy instrument only under FTA. Thus, it supports the result
in Xu et al. (2016), who showed that privatization policy can play the role of commitment device to
encourage parties to agree to an FTA and thus, it can improve both domestic and global welfare.
Fourth, we examine and compare the maximum-revenue equilibrium with the optimum-welfare
3
equilibrium and show that the maximum-revenue privatization, combined with zero subsidy and
higher tariff, is higher than optimum-welfare privatization in international bilateral mixed markets.
Finally, the international bilateral equilibrium involves less degree of privatization level and lower
subsidy rate, even though it is jointly suboptimal from the viewpoint of global welfare. This result is
consistent with the result in Lee et al. (2013), who neither consider the subsidy nor FTA agreements.
The remainder of this paper is organized as follows. Section 2 introduces the basic model. In
section 3, we investigate four different regime choices of production subsidy and import tariff with
partial privatization under Cournot competition. In section 4, we examine the asymmetric choices of
two countries on trade instruments between subsidy and tariff, compare the optimal equilibria with
four scenarios in a unilateral mixed market, compare the results under Stackelberg competition, and
investigate local optimum for maximum-revenue and global optimum for maximum-welfare. Section
5 concludes this paper.
2. The Model
Suppose that there are two countries: one is the home country (country 1) and the other is the
foreign country (country 2). The home country and foreign country both have symmetric duopoly
situations: each country has a state-owned enterprise (SOE) and a private enterprise (PE), which
producing homogeneous products. We assume that the domestic SOE produce output for its domestic
market only while the domestic PE can supply not only for domestic but also foreign markets. That is,
we consider PEs can export the same products to the other country and two countries are engaged in
intra-industry trade.4
Both governments adopt a complete set of trade policy instruments, including a production
subsidy ( 0)is per unit of output provided to the domestic firms and an import tariff ( 0)it per
unit of output imposed on the foreign firms. Let us denote the SOE’s outputs and the PE’s outputs in
country i as siq and hiq , while PE’s export outputs as eiq . The inverse demand functions of both
markets are the same and given by 1 ,i iP Q where the price of market i is denoted by Pi and the
output of market i is i si hi ejQ q q q where 1,2i j .
We assume that the cost functions of SOE and PE are quadratic5and given as 21
( )2
si siC q q and
21( ) ( )
2hi ei hi eiC q q q q . Then, the profits of the SOE and PE in country i are
2
i
1( )
2si i si siP s q q , ( 1 )
4 In reality, the domestic SOEs have significant market shares in sectors such as transportation, telecommunications, power
generation, electricity, finance, manufacturing, and other energy industries. Thus, for some governmental purposes such as to
stabilize domestic market prices, SOEs seldom participate in export. Existing literature also shows that international trade
will induce only the more productive private firms to enter the export market, while some less productive firms will continue
to produce only for the domestic market when export market entry costs exist (Melitz, 2003; Helpman et al. 2004) or cost
inefficiency of the SOE (Lee et al. 2013). In the Appendix, even though we allow for SOE to export, we can show that the
export outputs of the SOE are zero unless full privatization is achieved at equilibrium. 5 In the mixed market literature, asymmetric costs between SOE and PE proposed the desirability of privatization. See, for
example, Lee and Hwang (2003), Chang (2005), Lee (2006), and Wang et al. (2009). However, early studies of mixed
oligopoly, including De Fraja and Delbono (1989), Matsumura (1998), and Pal and White (1998), assumed the same
increasing marginal cost and showed that partial privatization in mixed oligopoly will improve the welfare.
4
2
i i
1( ) ( ) ( )
2pi i hi j j ei hi eiP s q P s t q q q . ( 2 )
The consumer surplus is denoted as 21
( )2
i iCS Q . And the social welfare is defined as the sum
of consumer surplus, domestic industry profits, import tariff revenues, i i ejT t q and production
subsidy, ( )i i si hi eiS s q q q :
i i si pi i iW CS T S . ( 3 )
The firms’ objective functions are subject to their ownership structures. We suppose that the PE,
which has characteristics of private property rights, maximizes its profits, while the SOE, which can
be partially (or fully) owned by the government. We assume that the manager of the SOE maximizes
the share-weighted objectives between both social welfare and profits6 , which are defined as
( 1 )i i si i iO W , where i indicates the tendency of the SOE to seek profits in the process of
privatization (or the shares owned by private investors).
In this paper, a two-stage game is constructed. In the first stage, both governments choose the
levels of tariff, subsidy and privatization to maximize their domestic social welfares. In the second
stage, the firms observe the levels of tariff, subsidy and privatization and then choose their output
levels.
3. The Policy Analysis
We investigate and compare four regime choices of production subsidy and import tariff, coupled
with partial privatization under Cournot competition: no trade instrument, production subsidy, import
tariff and dual trade instruments.
3.1. Dual trade instruments
We consider the general case that both governments adopt dual trade instruments of production
subsidy and import tariff with the privatization policy. In the second stage, the SOEs maximize their
objective functions, Oi, and the PEs maximize their own profits, pi , after observing the levels of
privatization. From the first-order conditions, we have the following equilibrium outputs of SOE and
PE:
3(20 7 2 5 5 ) (18 83 20 37 11 )1
(27 8 7 8 ) 3(2 12 4 5 )
i j i j i j i j i
si
i j i j j i j i j i jC
s s t t s s t tq
s s t t s s t t
,
3(5 12 4 10 10 ) (18 7 8 )1
(3 16 2 14 16 ) (6 4 4 5 )
i j i j i j i j i
hi
i j i j j i j i j i jC
s s t t s s t tq
s s t t s s t t
,
3( 5 11 5 20 ) ( 3 21 3 3 24 )1
( 18 20 26 11 37 ) 3( 2 4 4 5 )
i j i j i j i j i
ei
i j i j j i j i j i jC
s s t t s s t tq
s s t t s s t t
,
6 Partial public ownership was introduced by Bos (1991) and George and La Manna (1996). Matsumura (1998) formulated
theoretical analysis on the mixed market model and investigated the optimal degree of partial privatization. Lee and Hwang
(2003) incorporated the agency problem into his model and showed that partial privatization is generally optimal both in
public monopoly and in mixed market under moderate conditions.
5
where i =1,2 and 3(45 19 19 8 )C i j i j .
The market output and price of country i are
9(10 2 3 5 ) (18 50 8 )1
(33 5 22 17 5 ) (6 20 4 5 )
i j i i j i j i
i
i j i j j i j i j i jC
s s t s s t tQ
s s t t s s t t
,
9(5 2 3 5 ) (39 50 8 )1
(24 5 22 17 5 ) (18 20 4 5 )
i j i i j i j i
i
i j i j j i j i j i jC
s s t s s t tP
s s t t s s t t
.
The social welfare of country i is7
2 2 2 2
1 2 3 1 2 3 1 2 32
13(15 6 ) 6( ) ( 2 )
2i j j j j i j j i
C
W A A A B B B C C C
.
Let superscript “D*” denote the equilibrium outcome in dual trade instruments case. Then the
differentiation of iW with respect to i , is and it yields the following optimal degree of
privatization, subsidy and tariff rates:
* 2 1D
i , * 17 8 2
46
D
is
, * 11 7 2
138
D
it
. (4 )
Substituting the optimal degree of privatization, subsidy, and tariff rates into the above equations,
we obtain the outputs of SOEs and PEs, * 0.33D
siq , * 0.22D
hiq and * 0.07D
eiq . Note that
* * *D D D
si hi ejq q q which implies that the government will strategically use the SOE to act as trade
barriers and promote the domestic market competition for reaching a higher domestic social welfare.
It is also noteworthy that the marginal production cost of SOE is higher than that of the PE, which is
conferring cost disadvantages of export to the SOE at equilibrium. Then the market output and price
are * 0.62D
iQ and * 0.38D
iP . Finally, the optimal social welfare is * 0.331D
iW .
3.2. No trade instrument
We consider the case where both governments do not use any trade instruments but only adopt
the privatization policy to maximize their domestic social welfares. Let superscript “N*” denote the
equilibrium outcome under no trade instrument regime. Setting 0i j i jt t s s into the
equilibrium and welfare in the previous analysis, we can have the following optimal degree of
privatization:
* 13849 99
92
N
i
. (5)
Substituting the optimal degree of privatization into the above equations, we obtain the outputs
of SOEs and PEs, * 0.39N
siq and * * 0.12N N
hi eiq q . Then the market output and price are
* 0.63N
iQ and * 0.37N
iP . Finally, the optimal social welfare is * 0.327N
iW .
7 See Appendix II for the complete expression of the social welfare.
6
3.3. Production subsidy
We consider the case that both governments adopt a production subsidy instrument with the
privatization policy. Let superscript “S*” denote the equilibrium outcome under production subsidy
regime. Setting 0i jt t into the equilibrium and welfare in the previous analysis, we can have the
following optimal degree of privatization and subsidy rate:
* 2929 43
40
S
i
, * 8459 93 2929
21680
S
is
. ( 6 )
Substituting the optimal degree of privatization and subsidy rate into the above equations, we
obtain the outputs of SOEs and PEs, * 0.37S
siq and * * 0.16S S
hi eiq q . Then the market output and
price, * 0.69S
iQ and* 0.31S
iP . Finally, the optimal social welfare is * 0.332S
iW .
3.4. Import tariff
We consider the case that both governments adopt an import tariff instrument with the
privatization policy. Let superscript “T*” denote the equilibrium outcome under import tariff regime.
Setting 0i js s into the equilibrium and welfare in the previous analysis, we can have the
following optimal degree of privatization and tariff rates:
* 2513 41
32
T
i
, * 3516 47 2513
8553
T
it
. (7 )
Substituting the optimal degree of privatization and tariff rate into the above equations, we obtain
the outputs of SOEs and PEs, * 0.35T
siq , * 0.18T
hiq and * 0.05T
eiq . Then the market output and
price, * 0.58T
iQ and* 0.42T
iP . Finally, the optimal social welfare is * 0.324T
iW .
3.5. Comparisons
We compare the results of four different regime choices of production subsidy and import tariff,
coupled with partial privatization in the international bilateral mixed market.
Proposition 1: Under Cournot competition, the highest social welfare can be achieved when both
governments adopt a production subsidy policy only with partial privatization in the international
bilateral mixed market.
TABLE I: Comparisons under Cournot competition in the bilateral market
TABLE I shows the comparisons of equilibrium results under the international bilateral Cournot
7
competition. Three important remarks are noteworthy. First, both governments cannot achieve a
higher social welfare when they adopt the dual trade instruments simultaneously, i.e., * *0.331 0.332D S
i iW W . This is because the output substitution effect between the SOE and PE is
weakened while the welfare-reducing effect from the tariff is strengthened under the dual policy
regime. Thus, the equilibrium results of subsidy regime cannot be sustained when both governments
have an option to adopt the dual trade instruments when two countries can strategically change the
rates of subsidy and tariff together under Cournot competition.8 Accordingly, the government chooses
lower degree of privatization and higher subsidy rates to protect domestic welfare. This is the sharp
difference between the competitive equilibrium in the bilateral mixed market and the optimal
equilibrium in the unilateral mixed market such as Han (2012), which will be re-examined in the
following section. (See Proposition 2)
Second, this competitive equilibrium provides the prisoner’s dilemma situation and thus, the FTA
can work for solving this problem. That is, if two countries cooperate and adopt a subsidy instrument
only under free trade agreement, then both of them could achieve higher social welfare levels.
However, if two countries adopt the dual trade instruments of subsidy and tariff, then the social
welfares are lower than those under a single trade instrument with subsidy. Even without subsidy
policy under the framework of WTO, compared to the result in the import tariff only regime, the
social welfares are higher when both governments choose no trade instrument regime, * *0.327 0.324N T
i iW W . That is, both governments can achieve higher welfare levels when they
signed FTA which implies that FTA can work as a coordination device to solve the prisoner’s dilemma
in the bilateral mixed market. This result can be also applied to the asymmetric trade instruments case
where domestic and foreign governments adopt different trade instruments between subsidy and tariff,
which will be discussed in the next section. (See section 4.1)
Third, both governments cannot achieve the maximum welfare in the first-best allocation even
under the subsidy regime. When the government decides the direct allocation which maximizes its
domestic welfare, where the market price is equal to marginal production cost, both governments can
get the maximum welfare level of * 0.333iW , which is larger than * 0.332S
iW . It confirms that
privatization neutrality theorem does not hold when foreign competitor is included in the international
bilateral trade model under the different optimal subsidy/tariff regimes.9 That is, the effect of
privatization on welfare is affected by the response of the foreign country’s policy in bilateral trade.
Thus, strategic bilateral trade leads to a significantly different welfare comparison before and after the
imposition of production subsidy. In particular, the degree of privatization under subsidy regime
should be lower than that under tariff regime, which is also lower than that under dual trade
instruments.
8 It is easy to show that the equilibrium in subsidy regime is not an equilibrium in the dual-instrument regime. For this,
suppose that one country i sets the optimal subsidy, tariff, and privatization at the optimal levels in subsidy regime, i.e., * 0.28S
i , * 0.16S
is and * 0S
it . Then we can find the optimal responses of the other country j in dual-instrument regime
are * 0.39S
j , * 0S
js and * 0S
jt . Thus, the rsulting social welfare of each country is * 0.325iW and * 0.336jW ,
which induces country j to deviate from the results in subsidy regime. 9 Privatization neutrality theorem states that privatization does not affect welfare regardless of time structure, competition
mode, the number of firms, product differentiation, and the degree of privatization under the optimal tax-subsidy policy. This
well-known theorem has been discussed in White (1996), Poyago-Theotoky (2001), Tomaru (2006), Hashimzade et al.
(2007) and Matsumura and Okumura (2013). However, if there are foreign competitors, privatization matters on the welfare
even under the optimal tax-subsidy policy. See, for example, Matsumura and Tomaru (2012).
8
4. Discussions
In this section, we first analyze the equilibrium with asymmetric trade instruments where
domestic and foreign governments adopt different trade instruments. We next compare the
equilibrium outcomes in the bilateral mixed market with the previous results under a unilateral mixed
market. We then investigate the results under Stackelberg leadership of SOE and compare them with
those under Cournot competition. Finally, we investigate the local optimum for maximum-revenue
and global optimum for maximum-welfare under Cournot competition.
4.1. Asymmetric trade instruments between subsidy and tariff
We have considered the symmetric trade instruments case where domestic and foreign
governments adopt same trade instruments between subsidy and tariff in section 3. Here we analyze
the asymmetric situation where two governments adopt different trade instruments in the international
bilateral mixed market, and provide the similar situation of prisoner’s dilemma game.
Suppose that domestic government adopts a positive production subsidy to its domestic SOE and
PE, ( 0)is , and foreign government adopts a positive import tariff, ( 0)jt . Then, the profit
functions of SOE and PE, and the social welfare of domestic and foreign countries are as follows:
2
i
1( )
2si i si siP s q q ,
21
2sj j sj sjP q q ,
2
i i
1( ) ( ) ( )
2pi i hi j j ei hi eiP s q P s t q q q ,
21( )
2pj j hj i ej hj ejP q Pq q q ,
( )i i si pi i si hi eiW CS s q q q , j j sj pj j eiW CS t q .
Let superscript “A*” denote the equilibrium outcome in this asymmetric trade instruments case.
The first-order conditions provide the following optimal degree of privatization, subsidy and tariff: * 0.262A
i ,* 0.314A
j , * 0.148A
is and * 0.171A
jt . The optimal privatization level of country i
which adopts product subsidy is lower than that of country j which adopts import tariff, * *A A
i j .
Also, optimal subsidy and tariff levels of both countries are higher than those under dual symmetric
policy instruments, while optimal privatization is lower than that under symmetric dual policy
instruments, * *A D
i is s , * *A D
i it t and * *A D
i i .
Substituting them into the equilibrium outputs yields the optimal market output and price in the
two countries, * 0.656A
iQ , * 0.596A
jQ , * 0.344A
iP and * 0.404A
jP . Then, the resulting social
welfare are * 0.322A
iW and * 0.337A
jW . Note that under asymmetric trade instruments, foreign
government which adopts an import tariff with privatization policy can achieve a higher social welfare
than that under symmetric subsidy in TABLE I, i.e., * *( 0, 0) 0.337 0.332A S
j i j jW W . Thus,
the government which adopts an import tariff policy under asymmetric trade instruments will be better
off than that under symmetry trade instrument. However, this asymmetric trade instrument will harm
the other country which adopts a production subsidy only and thus, will make the other country to
choose tariff, i.e., * *( 0, 0) 0.322 0.324A T
i i j iW W . It also yields the prisoner’s dilemma
situation: if both countries cooperate to choose the subsidy-only policy with partial privatization, then
9
both can get higher social welfares. However, the government under asymmetric trade instruments
situation will rush to adopt the import tariff in order to obtain a higher social welfare which leads the
equilibrium of the symmetric import tariff only with partial privatization. (See footnote 7.)
4.2. Comparison with unilateral mixed market
We examine the equilibria under production subsidy, import tariff, and dual trade instruments
choices in the international unilateral mixed market, where there exists one home country in which the
SOE compete with the domestic PE and one foreign PE. In particular, from the previous models, if we
set 0,sjq 0,hjq 0,eiq 0,j 0js and t j , then we can have the same results with those
in Han (2012), which are shown in TABLE II.
TABLE II: Comparisons under Cournot competition in the unilateral market
i it is iW
Subsidy 1 0 0.40 0.340
Tariff 0.36 0.23 0 0.336
Dual instruments 1 0.15 0.31 0.346
Han (2012) showed that the government prefers the product subsidy to the import tariff (p.589,
Proposition 2), and the social welfare is higher when it simultaneously adopts dual trade instruments
of subsidy and tariff than that when it only adopts a single-trade instrument whether it is subsidy or
tariff (p.591, Proposition 4). Furthermore, it is shown that the optimal regime choice is that the SOE is
privatized completely and the dual trade instrument of subsidy and tariff is used jointly in a unilateral
mixed market. Therefore, it also confirms that privatization neutrality theorem does not hold when
foreign competition is included under the different optimal subsidy/tariff regimes.
The reasoning for the above results is as follows: the role of a subsidy is expanding the total
industry output while the role of a tariff is reducing the output of foreign firms. Thus, a subsidy
improves the social welfare through increasing consumer surplus while a tariff improves the social
welfare through gaining tariff revenue. However, unlike subsidy, the tariff lowers the total industry
output and thus lowers consumer surplus. It implies that welfare-maximizing government prefers the
product subsidy to the import tariff.10 Comparing the effects of subsidy and tariff, we can find that
subsidy can shift production from the high-cost SOE to the low-cost PE, and thus subsidy can induce
welfare-improving output substitution effect between the SOE and domestic PE. Accordingly, the
government chooses a higher subsidy and a lower tariff, coupled with complete privatization.
However, in the bilateral mixed market where the PEs can export their products to the opposite
country, the reduced output of the SOE through privatization will be substituted by the foreign PE and
the increased exporting output of domestic PE will increase the cost of domestic PE. Thus,
privatization will reduce the welfare-improving output substitution effect. It implies that both
governments will choose the partial privatization in the bilateral mixed market and the effectiveness
of free trade policy is significant, which is sharply contrasted to the previous results of Han (2012) in
a unilateral mixed market. In particular, the strategic interaction under competitive equilibrium in the
10 This result parallels the analysis of Pal and White (1998), who found that the subsidy is a better choice for the government
when the cost parameter is not so large.
10
bilateral mixed market requires a less subsidy and no tariff with partial privatization.
Proposition 2: Under Cournot competition, a lower production subsidy with partial privatization is
the best choice in the international bilateral mixed market while dual trade instruments of higher
subsidy and higher tariff with full privatization is the best choice in a unilateral mixed market.
4.3. Stackelberg competition
Then, we investigate four different regime choices of production subsidy and import tariff under
Stackelberg competition in the international bilateral mixed market where the semi-pubic firm acts as
a leader.11 Let superscript “SD*”, “SN*”, “SS*” and “ST*” denote the equilibrium outcomes under
Stackelberg competition, respectively.
We first consider the case in which both governments adopt dual trade instments with the
privatization simultaneously. Under Stackelberg competition with a dominant semi-public firm, after
given the announced levels of θi, the SOE maximize Oi and then the PE maximize pi sequentially,
observing the levels of privatization and the output levels of the SOE.
In the third stage, maximizing pi for a given θi and siq , we can obtain the output of each PE
3(1 ) 4 4
15
i j si sj i j
hi
t t q q s sq
,
3 4 4 2 7
15
sj si i j i j
ei
q q s s t tq
.
In the second stage, each SOE sets its output for given θi, anticipating the reaction of the
domestic and foreign followers as given. We get the solution